We look at the division of 641577 by 15 
Our goal is to divide 641577 by 15.

On to step 1:
When dividing 6 by 15, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 15

Step 2:
The number 15 fits into 64 4 times, leaving a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
If we take 60 away from 64, we end up with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 15

Moving on to step 3:
15 can be fit into 41 2 times, resulting in a remainder of 11.
Use 2 as the next digit of our solution. 
Result so far: 42.0
The remainder is 11 after subtracting 30 from 41.
Bring next digit (5) of the dividend behind the 11 and repeat the process: 115 / 15

Step 4:
115 divided by 15 is 7 with a remainder of 10.
The next digit of our result is 7. 
Result so far: 427.0
If we take 105 away from 115, we end up with 10.
Include the next digit (7) from the dividend after 10, then repeat: 107 / 15

Step 5:
If we divide 107 by 15, we get 7 and a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 4277.0
Subtracting 105 from 107 leaves us with 2.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 15

Going ahead to step 6:
15 can be fit into 27 1 times, resulting in a remainder of 12.
Use 1 as the next digit of our solution. 
Result so far: 42771.0
Deduct 15 from 27 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 7:
When dividing 120 by 15, we get 8 with a remainder of 0.
Record the quotient 8 as the next digit in the result. 
Result so far: 42771.8
If we subtract 120 from 120, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 8:
If we divide 0 by 15, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 42771.8
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 9:
The number 15 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 42771.8
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 42771.8 with a balance of 0.0.